/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date:        15. February 2012
* $Revision: 	V1.1.0
*
* Project: 	    CMSIS DSP Library
* Title:	    arm_cfft_radix4_q31.c
*
* Description:	This file has function definition of Radix-4 FFT & IFFT function and
*				In-place bit reversal using bit reversal table
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.1.0 2012/02/15
*    Updated with more optimizations, bug fixes and minor API changes.
*
* Version 1.0.10 2011/7/15
*    Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
*    Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
*    Documentation updated.
*
* Version 1.0.1 2010/10/05
*    Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
*    Production release and review comments incorporated.
*
* Version 0.0.5  2010/04/26
* 	 incorporated review comments and updated with latest CMSIS layer
*
* Version 0.0.3  2010/03/10
*    Initial version
* -------------------------------------------------------------------- */
#include "arm_math.h"


/**
 * @ingroup groupTransforms
 */

/**
 * @addtogroup Radix4_CFFT_CIFFT
 * @{
 */

/**
 * @details
 * @brief Processing function for the Q31 CFFT/CIFFT.
 * @param[in]      *S    points to an instance of the Q31 CFFT/CIFFT structure.
 * @param[in, out] *pSrc points to the complex data buffer of size <code>2*fftLen</code>. Processing occurs in-place.
 * @return none.
 *
 * \par Input and output formats:
 * \par
 * Internally input is downscaled by 2 for every stage to avoid saturations inside CFFT/CIFFT process.
 * Hence the output format is different for different FFT sizes.
 * The input and output formats for different FFT sizes and number of bits to upscale are mentioned in the tables below for CFFT and CIFFT:
 * \par
 * \image html CFFTQ31.gif "Input and Output Formats for Q31 CFFT"
 * \image html CIFFTQ31.gif "Input and Output Formats for Q31 CIFFT"
 *
 */

void arm_cfft_radix4_q31(
    const arm_cfft_radix4_instance_q31* S,
    q31_t* pSrc)
{
	if(S->ifftFlag == 1u) {
		/* Complex IFFT radix-4 */
		arm_radix4_butterfly_inverse_q31(pSrc, S->fftLen, S->pTwiddle,
		                                 S->twidCoefModifier);
	} else {
		/* Complex FFT radix-4 */
		arm_radix4_butterfly_q31(pSrc, S->fftLen, S->pTwiddle,
		                         S->twidCoefModifier);
	}


	if(S->bitReverseFlag == 1u) {
		/*  Bit Reversal */
		arm_bitreversal_q31(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable);
	}

}

/**
 * @} end of Radix4_CFFT_CIFFT group
 */

/*
* Radix-4 FFT algorithm used is :
*
* Input real and imaginary data:
* x(n) = xa + j * ya
* x(n+N/4 ) = xb + j * yb
* x(n+N/2 ) = xc + j * yc
* x(n+3N 4) = xd + j * yd
*
*
* Output real and imaginary data:
* x(4r) = xa'+ j * ya'
* x(4r+1) = xb'+ j * yb'
* x(4r+2) = xc'+ j * yc'
* x(4r+3) = xd'+ j * yd'
*
*
* Twiddle factors for radix-4 FFT:
* Wn = co1 + j * (- si1)
* W2n = co2 + j * (- si2)
* W3n = co3 + j * (- si3)
*
*  Butterfly implementation:
* xa' = xa + xb + xc + xd
* ya' = ya + yb + yc + yd
* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1)
* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1)
* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2)
* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2)
* xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3)
* yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3)
*
*/

/**
 * @brief  Core function for the Q31 CFFT butterfly process.
 * @param[in, out] *pSrc            points to the in-place buffer of Q31 data type.
 * @param[in]      fftLen           length of the FFT.
 * @param[in]      *pCoef           points to twiddle coefficient buffer.
 * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
 * @return none.
 */

void arm_radix4_butterfly_q31(
    q31_t* pSrc,
    uint32_t fftLen,
    q31_t* pCoef,
    uint32_t twidCoefModifier)
{
	uint32_t n1, n2, ia1, ia2, ia3, i0, i1, i2, i3, j, k;
	q31_t t1, t2, r1, r2, s1, s2, co1, co2, co3, si1, si2, si3;

	q31_t xa, xb, xc, xd;
	q31_t ya, yb, yc, yd;
	q31_t xa_out, xb_out, xc_out, xd_out;
	q31_t ya_out, yb_out, yc_out, yd_out;

	q31_t* ptr1;
	q63_t xaya, xbyb, xcyc, xdyd;
	/* Total process is divided into three stages */

	/* process first stage, middle stages, & last stage */


	/* start of first stage process */

	/*  Initializations for the first stage */
	n2 = fftLen;
	n1 = n2;
	/* n2 = fftLen/4 */
	n2 >>= 2u;
	i0 = 0u;
	ia1 = 0u;

	j = n2;

	/*  Calculation of first stage */
	do {
		/*  index calculation for the input as, */
		/*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2u], pSrc[i0 + 3fftLen/4] */
		i1 = i0 + n2;
		i2 = i1 + n2;
		i3 = i2 + n2;

		/* input is in 1.31(q31) format and provide 4 guard bits for the input */

		/*  Butterfly implementation */
		/* xa + xc */
		r1 = (pSrc[(2u * i0)] >> 4u) + (pSrc[(2u * i2)] >> 4u);
		/* xa - xc */
		r2 = (pSrc[2u * i0] >> 4u) - (pSrc[2u * i2] >> 4u);

		/* xb + xd */
		t1 = (pSrc[2u * i1] >> 4u) + (pSrc[2u * i3] >> 4u);

		/* ya + yc */
		s1 = (pSrc[(2u * i0) + 1u] >> 4u) + (pSrc[(2u * i2) + 1u] >> 4u);
		/* ya - yc */
		s2 = (pSrc[(2u * i0) + 1u] >> 4u) - (pSrc[(2u * i2) + 1u] >> 4u);

		/* xa' = xa + xb + xc + xd */
		pSrc[2u * i0] = (r1 + t1);
		/* (xa + xc) - (xb + xd) */
		r1 = r1 - t1;
		/* yb + yd */
		t2 = (pSrc[(2u * i1) + 1u] >> 4u) + (pSrc[(2u * i3) + 1u] >> 4u);

		/* ya' = ya + yb + yc + yd */
		pSrc[(2u * i0) + 1u] = (s1 + t2);

		/* (ya + yc) - (yb + yd) */
		s1 = s1 - t2;

		/* yb - yd */
		t1 = (pSrc[(2u * i1) + 1u] >> 4u) - (pSrc[(2u * i3) + 1u] >> 4u);
		/* xb - xd */
		t2 = (pSrc[2u * i1] >> 4u) - (pSrc[2u * i3] >> 4u);

		/*  index calculation for the coefficients */
		ia2 = 2u * ia1;
		co2 = pCoef[ia2 * 2u];
		si2 = pCoef[(ia2 * 2u) + 1u];

		/* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
		pSrc[2u * i1] = (((int32_t)(((q63_t) r1 * co2) >> 32)) +
		                 ((int32_t)(((q63_t) s1 * si2) >> 32))) << 1u;

		/* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
		pSrc[(2u * i1) + 1u] = (((int32_t)(((q63_t) s1 * co2) >> 32)) -
		                        ((int32_t)(((q63_t) r1 * si2) >> 32))) << 1u;

		/* (xa - xc) + (yb - yd) */
		r1 = r2 + t1;
		/* (xa - xc) - (yb - yd) */
		r2 = r2 - t1;

		/* (ya - yc) - (xb - xd) */
		s1 = s2 - t2;
		/* (ya - yc) + (xb - xd) */
		s2 = s2 + t2;

		co1 = pCoef[ia1 * 2u];
		si1 = pCoef[(ia1 * 2u) + 1u];

		/* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
		pSrc[2u * i2] = (((int32_t)(((q63_t) r1 * co1) >> 32)) +
		                 ((int32_t)(((q63_t) s1 * si1) >> 32))) << 1u;

		/* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
		pSrc[(2u * i2) + 1u] = (((int32_t)(((q63_t) s1 * co1) >> 32)) -
		                        ((int32_t)(((q63_t) r1 * si1) >> 32))) << 1u;

		/*  index calculation for the coefficients */
		ia3 = 3u * ia1;
		co3 = pCoef[ia3 * 2u];
		si3 = pCoef[(ia3 * 2u) + 1u];

		/* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
		pSrc[2u * i3] = (((int32_t)(((q63_t) r2 * co3) >> 32)) +
		                 ((int32_t)(((q63_t) s2 * si3) >> 32))) << 1u;

		/* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
		pSrc[(2u * i3) + 1u] = (((int32_t)(((q63_t) s2 * co3) >> 32)) -
		                        ((int32_t)(((q63_t) r2 * si3) >> 32))) << 1u;

		/*  Twiddle coefficients index modifier */
		ia1 = ia1 + twidCoefModifier;

		/*  Updating input index */
		i0 = i0 + 1u;

	} while(--j);

	/* end of first stage process */

	/* data is in 5.27(q27) format */


	/* start of Middle stages process */


	/* each stage in middle stages provides two down scaling of the input */

	twidCoefModifier <<= 2u;


	for(k = fftLen / 4u; k > 4u; k >>= 2u) {
		/*  Initializations for the first stage */
		n1 = n2;
		n2 >>= 2u;
		ia1 = 0u;

		/*  Calculation of first stage */
		for(j = 0u; j <= (n2 - 1u); j++) {
			/*  index calculation for the coefficients */
			ia2 = ia1 + ia1;
			ia3 = ia2 + ia1;
			co1 = pCoef[ia1 * 2u];
			si1 = pCoef[(ia1 * 2u) + 1u];
			co2 = pCoef[ia2 * 2u];
			si2 = pCoef[(ia2 * 2u) + 1u];
			co3 = pCoef[ia3 * 2u];
			si3 = pCoef[(ia3 * 2u) + 1u];
			/*  Twiddle coefficients index modifier */
			ia1 = ia1 + twidCoefModifier;

			for(i0 = j; i0 < fftLen; i0 += n1) {
				/*  index calculation for the input as, */
				/*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2u], pSrc[i0 + 3fftLen/4] */
				i1 = i0 + n2;
				i2 = i1 + n2;
				i3 = i2 + n2;

				/*  Butterfly implementation */
				/* xa + xc */
				r1 = pSrc[2u * i0] + pSrc[2u * i2];
				/* xa - xc */
				r2 = pSrc[2u * i0] - pSrc[2u * i2];

				/* ya + yc */
				s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
				/* ya - yc */
				s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];

				/* xb + xd */
				t1 = pSrc[2u * i1] + pSrc[2u * i3];

				/* xa' = xa + xb + xc + xd */
				pSrc[2u * i0] = (r1 + t1) >> 2u;
				/* xa + xc -(xb + xd) */
				r1 = r1 - t1;

				/* yb + yd */
				t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
				/* ya' = ya + yb + yc + yd */
				pSrc[(2u * i0) + 1u] = (s1 + t2) >> 2u;

				/* (ya + yc) - (yb + yd) */
				s1 = s1 - t2;

				/* (yb - yd) */
				t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
				/* (xb - xd) */
				t2 = pSrc[2u * i1] - pSrc[2u * i3];

				/* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
				pSrc[2u * i1] = (((int32_t)(((q63_t) r1 * co2) >> 32)) +
				                 ((int32_t)(((q63_t) s1 * si2) >> 32))) >> 1u;

				/* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
				pSrc[(2u * i1) + 1u] = (((int32_t)(((q63_t) s1 * co2) >> 32)) -
				                        ((int32_t)(((q63_t) r1 * si2) >> 32))) >> 1u;

				/* (xa - xc) + (yb - yd) */
				r1 = r2 + t1;
				/* (xa - xc) - (yb - yd) */
				r2 = r2 - t1;

				/* (ya - yc) -  (xb - xd) */
				s1 = s2 - t2;
				/* (ya - yc) +  (xb - xd) */
				s2 = s2 + t2;

				/* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
				pSrc[2u * i2] = (((int32_t)(((q63_t) r1 * co1) >> 32)) +
				                 ((int32_t)(((q63_t) s1 * si1) >> 32))) >> 1u;

				/* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
				pSrc[(2u * i2) + 1u] = (((int32_t)(((q63_t) s1 * co1) >> 32)) -
				                        ((int32_t)(((q63_t) r1 * si1) >> 32))) >> 1u;

				/* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
				pSrc[2u * i3] = (((int32_t)(((q63_t) r2 * co3) >> 32)) +
				                 ((int32_t)(((q63_t) s2 * si3) >> 32))) >> 1u;

				/* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
				pSrc[(2u * i3) + 1u] = (((int32_t)(((q63_t) s2 * co3) >> 32)) -
				                        ((int32_t)(((q63_t) r2 * si3) >> 32))) >> 1u;
			}
		}

		twidCoefModifier <<= 2u;
	}

	/* End of Middle stages process */

	/* data is in 11.21(q21) format for the 1024 point as there are 3 middle stages */
	/* data is in 9.23(q23) format for the 256 point as there are 2 middle stages */
	/* data is in 7.25(q25) format for the 64 point as there are 1 middle stage */
	/* data is in 5.27(q27) format for the 16 point as there are no middle stages */


	/* start of Last stage process */
	/*  Initializations for the last stage */
	j = fftLen >> 2;
	ptr1 = &pSrc[0];

	/*  Calculations of last stage */
	do {

#ifndef ARM_MATH_BIG_ENDIAN

		/* Read xa (real), ya(imag) input */
		xaya = *__SIMD64(ptr1)++;
		xa = (q31_t) xaya;
		ya = (q31_t)(xaya >> 32);

		/* Read xb (real), yb(imag) input */
		xbyb = *__SIMD64(ptr1)++;
		xb = (q31_t) xbyb;
		yb = (q31_t)(xbyb >> 32);

		/* Read xc (real), yc(imag) input */
		xcyc = *__SIMD64(ptr1)++;
		xc = (q31_t) xcyc;
		yc = (q31_t)(xcyc >> 32);

		/* Read xc (real), yc(imag) input */
		xdyd = *__SIMD64(ptr1)++;
		xd = (q31_t) xdyd;
		yd = (q31_t)(xdyd >> 32);

#else

		/* Read xa (real), ya(imag) input */
		xaya = *__SIMD64(ptr1)++;
		ya = (q31_t) xaya;
		xa = (q31_t)(xaya >> 32);

		/* Read xb (real), yb(imag) input */
		xbyb = *__SIMD64(ptr1)++;
		yb = (q31_t) xbyb;
		xb = (q31_t)(xbyb >> 32);

		/* Read xc (real), yc(imag) input */
		xcyc = *__SIMD64(ptr1)++;
		yc = (q31_t) xcyc;
		xc = (q31_t)(xcyc >> 32);

		/* Read xc (real), yc(imag) input */
		xdyd = *__SIMD64(ptr1)++;
		yd = (q31_t) xdyd;
		xd = (q31_t)(xdyd >> 32);


#endif

		/* xa' = xa + xb + xc + xd */
		xa_out = xa + xb + xc + xd;

		/* ya' = ya + yb + yc + yd */
		ya_out = ya + yb + yc + yd;

		/* pointer updation for writing */
		ptr1 = ptr1 - 8u;

		/* writing xa' and ya' */
		*ptr1++ = xa_out;
		*ptr1++ = ya_out;

		xc_out = (xa - xb + xc - xd);
		yc_out = (ya - yb + yc - yd);

		/* writing xc' and yc' */
		*ptr1++ = xc_out;
		*ptr1++ = yc_out;

		xb_out = (xa + yb - xc - yd);
		yb_out = (ya - xb - yc + xd);

		/* writing xb' and yb' */
		*ptr1++ = xb_out;
		*ptr1++ = yb_out;

		xd_out = (xa - yb - xc + yd);
		yd_out = (ya + xb - yc - xd);

		/* writing xd' and yd' */
		*ptr1++ = xd_out;
		*ptr1++ = yd_out;


	} while(--j);

	/* output is in 11.21(q21) format for the 1024 point */
	/* output is in 9.23(q23) format for the 256 point */
	/* output is in 7.25(q25) format for the 64 point */
	/* output is in 5.27(q27) format for the 16 point */

	/* End of last stage process */

}


/**
 * @brief  Core function for the Q31 CIFFT butterfly process.
 * @param[in, out] *pSrc            points to the in-place buffer of Q31 data type.
 * @param[in]      fftLen           length of the FFT.
 * @param[in]      *pCoef           points to twiddle coefficient buffer.
 * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
 * @return none.
 */


/*
* Radix-4 IFFT algorithm used is :
*
* CIFFT uses same twiddle coefficients as CFFT Function
*  x[k] = x[n] + (j)k * x[n + fftLen/4] + (-1)k * x[n+fftLen/2] + (-j)k * x[n+3*fftLen/4]
*
*
* IFFT is implemented with following changes in equations from FFT
*
* Input real and imaginary data:
* x(n) = xa + j * ya
* x(n+N/4 ) = xb + j * yb
* x(n+N/2 ) = xc + j * yc
* x(n+3N 4) = xd + j * yd
*
*
* Output real and imaginary data:
* x(4r) = xa'+ j * ya'
* x(4r+1) = xb'+ j * yb'
* x(4r+2) = xc'+ j * yc'
* x(4r+3) = xd'+ j * yd'
*
*
* Twiddle factors for radix-4 IFFT:
* Wn = co1 + j * (si1)
* W2n = co2 + j * (si2)
* W3n = co3 + j * (si3)

* The real and imaginary output values for the radix-4 butterfly are
* xa' = xa + xb + xc + xd
* ya' = ya + yb + yc + yd
* xb' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1)
* yb' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1)
* xc' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2)
* yc' = (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2)
* xd' = (xa+yb-xc-yd)* co3 - (ya-xb-yc+xd)* (si3)
* yd' = (ya-xb-yc+xd)* co3 + (xa+yb-xc-yd)* (si3)
*
*/

void arm_radix4_butterfly_inverse_q31(
    q31_t* pSrc,
    uint32_t fftLen,
    q31_t* pCoef,
    uint32_t twidCoefModifier)
{
	uint32_t n1, n2, ia1, ia2, ia3, i0, i1, i2, i3, j, k;
	q31_t t1, t2, r1, r2, s1, s2, co1, co2, co3, si1, si2, si3;
	q31_t xa, xb, xc, xd;
	q31_t ya, yb, yc, yd;
	q31_t xa_out, xb_out, xc_out, xd_out;
	q31_t ya_out, yb_out, yc_out, yd_out;

	q31_t* ptr1;
	q63_t xaya, xbyb, xcyc, xdyd;

	/* input is be 1.31(q31) format for all FFT sizes */
	/* Total process is divided into three stages */
	/* process first stage, middle stages, & last stage */

	/* Start of first stage process */

	/* Initializations for the first stage */
	n2 = fftLen;
	n1 = n2;
	/* n2 = fftLen/4 */
	n2 >>= 2u;
	i0 = 0u;
	ia1 = 0u;

	j = n2;

	do {

		/* input is in 1.31(q31) format and provide 4 guard bits for the input */

		/*  index calculation for the input as, */
		/*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2u], pSrc[i0 + 3fftLen/4] */
		i1 = i0 + n2;
		i2 = i1 + n2;
		i3 = i2 + n2;

		/*  Butterfly implementation */
		/* xa + xc */
		r1 = (pSrc[2u * i0] >> 4u) + (pSrc[2u * i2] >> 4u);
		/* xa - xc */
		r2 = (pSrc[2u * i0] >> 4u) - (pSrc[2u * i2] >> 4u);

		/* xb + xd */
		t1 = (pSrc[2u * i1] >> 4u) + (pSrc[2u * i3] >> 4u);

		/* ya + yc */
		s1 = (pSrc[(2u * i0) + 1u] >> 4u) + (pSrc[(2u * i2) + 1u] >> 4u);
		/* ya - yc */
		s2 = (pSrc[(2u * i0) + 1u] >> 4u) - (pSrc[(2u * i2) + 1u] >> 4u);

		/* xa' = xa + xb + xc + xd */
		pSrc[2u * i0] = (r1 + t1);
		/* (xa + xc) - (xb + xd) */
		r1 = r1 - t1;
		/* yb + yd */
		t2 = (pSrc[(2u * i1) + 1u] >> 4u) + (pSrc[(2u * i3) + 1u] >> 4u);
		/* ya' = ya + yb + yc + yd */
		pSrc[(2u * i0) + 1u] = (s1 + t2);

		/* (ya + yc) - (yb + yd) */
		s1 = s1 - t2;

		/* yb - yd */
		t1 = (pSrc[(2u * i1) + 1u] >> 4u) - (pSrc[(2u * i3) + 1u] >> 4u);
		/* xb - xd */
		t2 = (pSrc[2u * i1] >> 4u) - (pSrc[2u * i3] >> 4u);

		/*  index calculation for the coefficients */
		ia2 = 2u * ia1;
		co2 = pCoef[ia2 * 2u];
		si2 = pCoef[(ia2 * 2u) + 1u];

		/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
		pSrc[2u * i1] = (((int32_t)(((q63_t) r1 * co2) >> 32)) -
		                 ((int32_t)(((q63_t) s1 * si2) >> 32))) << 1u;

		/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
		pSrc[2u * i1 + 1u] = (((int32_t)(((q63_t) s1 * co2) >> 32)) +
		                      ((int32_t)(((q63_t) r1 * si2) >> 32))) << 1u;

		/* (xa - xc) - (yb - yd) */
		r1 = r2 - t1;
		/* (xa - xc) + (yb - yd) */
		r2 = r2 + t1;

		/* (ya - yc) + (xb - xd) */
		s1 = s2 + t2;
		/* (ya - yc) - (xb - xd) */
		s2 = s2 - t2;

		co1 = pCoef[ia1 * 2u];
		si1 = pCoef[(ia1 * 2u) + 1u];

		/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
		pSrc[2u * i2] = (((int32_t)(((q63_t) r1 * co1) >> 32)) -
		                 ((int32_t)(((q63_t) s1 * si1) >> 32))) << 1u;

		/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
		pSrc[(2u * i2) + 1u] = (((int32_t)(((q63_t) s1 * co1) >> 32)) +
		                        ((int32_t)(((q63_t) r1 * si1) >> 32))) << 1u;

		/*  index calculation for the coefficients */
		ia3 = 3u * ia1;
		co3 = pCoef[ia3 * 2u];
		si3 = pCoef[(ia3 * 2u) + 1u];

		/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
		pSrc[2u * i3] = (((int32_t)(((q63_t) r2 * co3) >> 32)) -
		                 ((int32_t)(((q63_t) s2 * si3) >> 32))) << 1u;

		/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
		pSrc[(2u * i3) + 1u] = (((int32_t)(((q63_t) s2 * co3) >> 32)) +
		                        ((int32_t)(((q63_t) r2 * si3) >> 32))) << 1u;

		/*  Twiddle coefficients index modifier */
		ia1 = ia1 + twidCoefModifier;

		/*  Updating input index */
		i0 = i0 + 1u;

	} while(--j);

	/* data is in 5.27(q27) format */
	/* each stage provides two down scaling of the input */


	/* Start of Middle stages process */

	twidCoefModifier <<= 2u;

	/*  Calculation of second stage to excluding last stage */
	for(k = fftLen / 4u; k > 4u; k >>= 2u) {
		/*  Initializations for the first stage */
		n1 = n2;
		n2 >>= 2u;
		ia1 = 0u;

		for(j = 0; j <= (n2 - 1u); j++) {
			/*  index calculation for the coefficients */
			ia2 = ia1 + ia1;
			ia3 = ia2 + ia1;
			co1 = pCoef[ia1 * 2u];
			si1 = pCoef[(ia1 * 2u) + 1u];
			co2 = pCoef[ia2 * 2u];
			si2 = pCoef[(ia2 * 2u) + 1u];
			co3 = pCoef[ia3 * 2u];
			si3 = pCoef[(ia3 * 2u) + 1u];
			/*  Twiddle coefficients index modifier */
			ia1 = ia1 + twidCoefModifier;

			for(i0 = j; i0 < fftLen; i0 += n1) {
				/*  index calculation for the input as, */
				/*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2u], pSrc[i0 + 3fftLen/4] */
				i1 = i0 + n2;
				i2 = i1 + n2;
				i3 = i2 + n2;

				/*  Butterfly implementation */
				/* xa + xc */
				r1 = pSrc[2u * i0] + pSrc[2u * i2];
				/* xa - xc */
				r2 = pSrc[2u * i0] - pSrc[2u * i2];

				/* ya + yc */
				s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
				/* ya - yc */
				s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];

				/* xb + xd */
				t1 = pSrc[2u * i1] + pSrc[2u * i3];

				/* xa' = xa + xb + xc + xd */
				pSrc[2u * i0] = (r1 + t1) >> 2u;
				/* xa + xc -(xb + xd) */
				r1 = r1 - t1;
				/* yb + yd */
				t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
				/* ya' = ya + yb + yc + yd */
				pSrc[(2u * i0) + 1u] = (s1 + t2) >> 2u;

				/* (ya + yc) - (yb + yd) */
				s1 = s1 - t2;

				/* (yb - yd) */
				t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
				/* (xb - xd) */
				t2 = pSrc[2u * i1] - pSrc[2u * i3];

				/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
				pSrc[2u * i1] = (((int32_t)(((q63_t) r1 * co2) >> 32u)) -
				                 ((int32_t)(((q63_t) s1 * si2) >> 32u))) >> 1u;

				/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
				pSrc[(2u * i1) + 1u] =
				    (((int32_t)(((q63_t) s1 * co2) >> 32u)) +
				     ((int32_t)(((q63_t) r1 * si2) >> 32u))) >> 1u;

				/* (xa - xc) - (yb - yd) */
				r1 = r2 - t1;
				/* (xa - xc) + (yb - yd) */
				r2 = r2 + t1;

				/* (ya - yc) +  (xb - xd) */
				s1 = s2 + t2;
				/* (ya - yc) -  (xb - xd) */
				s2 = s2 - t2;

				/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
				pSrc[2u * i2] = (((int32_t)(((q63_t) r1 * co1) >> 32)) -
				                 ((int32_t)(((q63_t) s1 * si1) >> 32))) >> 1u;

				/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
				pSrc[(2u * i2) + 1u] = (((int32_t)(((q63_t) s1 * co1) >> 32)) +
				                        ((int32_t)(((q63_t) r1 * si1) >> 32))) >> 1u;

				/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
				pSrc[(2u * i3)] = (((int32_t)(((q63_t) r2 * co3) >> 32)) -
				                   ((int32_t)(((q63_t) s2 * si3) >> 32))) >> 1u;

				/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
				pSrc[(2u * i3) + 1u] = (((int32_t)(((q63_t) s2 * co3) >> 32)) +
				                        ((int32_t)(((q63_t) r2 * si3) >> 32))) >> 1u;
			}
		}

		twidCoefModifier <<= 2u;
	}

	/* End of Middle stages process */

	/* data is in 11.21(q21) format for the 1024 point as there are 3 middle stages */
	/* data is in 9.23(q23) format for the 256 point as there are 2 middle stages */
	/* data is in 7.25(q25) format for the 64 point as there are 1 middle stage */
	/* data is in 5.27(q27) format for the 16 point as there are no middle stages */


	/* Start of last stage process */


	/*  Initializations for the last stage */
	j = fftLen >> 2;
	ptr1 = &pSrc[0];

	/*  Calculations of last stage */
	do {
#ifndef ARM_MATH_BIG_ENDIAN
		/* Read xa (real), ya(imag) input */
		xaya = *__SIMD64(ptr1)++;
		xa = (q31_t) xaya;
		ya = (q31_t)(xaya >> 32);

		/* Read xb (real), yb(imag) input */
		xbyb = *__SIMD64(ptr1)++;
		xb = (q31_t) xbyb;
		yb = (q31_t)(xbyb >> 32);

		/* Read xc (real), yc(imag) input */
		xcyc = *__SIMD64(ptr1)++;
		xc = (q31_t) xcyc;
		yc = (q31_t)(xcyc >> 32);

		/* Read xc (real), yc(imag) input */
		xdyd = *__SIMD64(ptr1)++;
		xd = (q31_t) xdyd;
		yd = (q31_t)(xdyd >> 32);

#else

		/* Read xa (real), ya(imag) input */
		xaya = *__SIMD64(ptr1)++;
		ya = (q31_t) xaya;
		xa = (q31_t)(xaya >> 32);

		/* Read xb (real), yb(imag) input */
		xbyb = *__SIMD64(ptr1)++;
		yb = (q31_t) xbyb;
		xb = (q31_t)(xbyb >> 32);

		/* Read xc (real), yc(imag) input */
		xcyc = *__SIMD64(ptr1)++;
		yc = (q31_t) xcyc;
		xc = (q31_t)(xcyc >> 32);

		/* Read xc (real), yc(imag) input */
		xdyd = *__SIMD64(ptr1)++;
		yd = (q31_t) xdyd;
		xd = (q31_t)(xdyd >> 32);


#endif

		/* xa' = xa + xb + xc + xd */
		xa_out = xa + xb + xc + xd;

		/* ya' = ya + yb + yc + yd */
		ya_out = ya + yb + yc + yd;

		/* pointer updation for writing */
		ptr1 = ptr1 - 8u;

		/* writing xa' and ya' */
		*ptr1++ = xa_out;
		*ptr1++ = ya_out;

		xc_out = (xa - xb + xc - xd);
		yc_out = (ya - yb + yc - yd);

		/* writing xc' and yc' */
		*ptr1++ = xc_out;
		*ptr1++ = yc_out;

		xb_out = (xa - yb - xc + yd);
		yb_out = (ya + xb - yc - xd);

		/* writing xb' and yb' */
		*ptr1++ = xb_out;
		*ptr1++ = yb_out;

		xd_out = (xa + yb - xc - yd);
		yd_out = (ya - xb - yc + xd);

		/* writing xd' and yd' */
		*ptr1++ = xd_out;
		*ptr1++ = yd_out;


	} while(--j);

	/* output is in 11.21(q21) format for the 1024 point */
	/* output is in 9.23(q23) format for the 256 point */
	/* output is in 7.25(q25) format for the 64 point */
	/* output is in 5.27(q27) format for the 16 point */

	/* End of last stage process */
}
